2024 NUTRIM microbiome & metabolome workshop
Read, copy, and run each section of this walkthrough in the practical-2-notebook.qmd on posit.cloud.
Create code chunks to store and run code, and write notes alongside the code about what you are doing.
Does the bacterial gut microbiota composition of IBD-diagnosed patients differ from the control patients?
Diversity: Is richness or diversity associated with IBD diagnosis?
Composition: Does overall bacterial microbiota composition associated with IBD diagnosis?
Taxa: Is the relative abundance of specific bacterial taxa (e.g. genera) associated with IBD diagnosis?
here() starts at /Users/david/Documents/git/R-projects/teaching/workshops/2024-NUTRIM-microbiome── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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✖ dplyr::filter() masks stats::filter()
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsmicroViz version 0.12.4 - Copyright (C) 2021-2024 David Barnett
! Website: https://david-barnett.github.io/microViz
✔ Useful? For citation details, run: `citation("microViz")`
✖ Silence? `suppressPackageStartupMessages(library(microViz))`You can cite this package as:
Patil, I. (2021). Visualizations with statistical details: The 'ggstatsplot' approach.
Journal of Open Source Software, 6(61), 3167, doi:10.21105/joss.03167Read the phyloseq we created in part 1.
If you did not finish part 1B, you will not have created the phyloseq object.
Don’t worry, I prepared a backup copy, which you can use instead.
You may also use this backup copy if you finished part 1B, but suspect you did something wrong.
Our research questions for this section are:
ps %>%
samdat_tbl() %>%
ggplot(aes(x = N_genera, y = diagnosis, color = diagnosis)) +
geom_boxplot(outliers = FALSE) +
geom_jitter(height = 0.15, alpha = 0.5) +
theme_classic()
You can use standard statistical testing on the richness values e.g. linear regression or ANOVA
richness_lm <- lm(data = samdat_tbl(ps), formula = N_genera ~ diagnosis)
anova(richness_lm)Analysis of Variance Table
Response: N_genera
Df Sum Sq Mean Sq F value Pr(>F)
diagnosis 2 1837.3 918.63 7.8329 0.0007448 ***
Residuals 87 10203.2 117.28
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1You could do also standard ANOVA post-hoc pairwise comparisons.
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = richness_lm)
$diagnosis
diff lwr upr p adj
CD-Other -5.275362 -12.81034 2.259620 0.2227571
UC-Other -10.782946 -17.36256 -4.203332 0.0005347
UC-CD -5.507583 -12.17836 1.163197 0.1261212Combine group comparison stats and plots in one go with ggstatsplot::ggbetweenstats()
ggbetweenstats(
data = samdat_tbl(ps), x = diagnosis, y = N_genera,
type = "parametric", p.adjust.method = "fdr", var.equal = TRUE,
bf.message = FALSE, results.subtitle = TRUE
)
Remember: a true measure of ecosystem diversity (e.g. Shannon index) will consider the richness and evenness of the ecosystem.
A rich ecosystem dominated by only one or two of its taxa is still a less diverse ecosystem than one with an even distribution of the same number of taxa.
We already computed Shannon diversity of genera and the effective Shannon in part 1B.
Here we will use the effective Shannon diversity \(e^H\) because of its more intuitive interpretation.
ps %>%
samdat_tbl() %>%
ggplot(aes(x = Effective_Shannon_Genus, y = diagnosis, color = diagnosis)) +
geom_boxplot(outliers = FALSE) +
geom_jitter(height = 0.2) +
theme_classic()
eShannon_lm <- lm(data = samdat_tbl(ps), formula = Effective_Shannon_Genus ~ diagnosis)
anova(eShannon_lm)Analysis of Variance Table
Response: Effective_Shannon_Genus
Df Sum Sq Mean Sq F value Pr(>F)
diagnosis 2 158.96 79.482 7.5185 0.0009731 ***
Residuals 87 919.73 10.572
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = eShannon_lm)
$diagnosis
diff lwr upr p adj
CD-Other -1.541564 -3.803828 0.7207006 0.2406931
UC-Other -3.170198 -5.145627 -1.1947686 0.0007080
UC-CD -1.628634 -3.631435 0.3741666 0.1339407You can get a tidy data frame of results using the broom::tidy function on various statistical model objects.
broom::tidy(eShannon_tukey)# A tibble: 3 × 7
term contrast null.value estimate conf.low conf.high adj.p.value
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 diagnosis CD-Other 0 -1.54 -3.80 0.721 0.241
2 diagnosis UC-Other 0 -3.17 -5.15 -1.19 0.000708
3 diagnosis UC-CD 0 -1.63 -3.63 0.374 0.134 This can be useful when you need to save your model output e.g. to Excel, to format for a table in your article.
broom::tidy(eShannon_tukey) %>% write_xlsx(here("practical-2/test-table.xlsx"))ggbetweenstats(
data = samdat_tbl(ps), x = diagnosis, y = Effective_Shannon_Genus,
type = "parametric", p.adjust.method = "fdr", var.equal = TRUE,
bf.message = FALSE, results.subtitle = TRUE
)
Our research questions for this section are:
In order to create a PCoA ordination - we need to first make two choices:
You heard about several commonly-used dissimilarity measures in the lecture. In the sections below, we will calculate a distance matrix with each one, and use each to plot a PCoA and test for diagnosis group differences with PERMANOVA.
An unweighted measure - based only on taxon presence or absence.
You must remember to run a “binary” transform on your data before computing “jaccard” distance.
psx_jaccardpsExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 178 taxa and 90 samples ]
sample_data() Sample Data: [ 90 samples by 20 sample variables ]
tax_table() Taxonomy Table: [ 178 taxa by 6 taxonomic ranks ]
otu_get(counts = TRUE) [ 178 taxa and 90 samples ]
psExtra info:
tax_agg = "Genus" tax_trans = "binary"
jaccard distance matrix of size 90
0.7173913 0.5588235 0.7241379 0.5483871 0.75 ...psx_jaccard %>%
ord_calc("PCoA") %>%
ord_plot(colour = "diagnosis") +
stat_ellipse(aes(colour = diagnosis)) +
coord_equal()
perm_jaccard <- psx_jaccard %>% dist_permanova(variables = "diagnosis")
perm_get(perm_jaccard)Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 2 1.970 0.08987 4.2954 0.001 ***
Residual 87 19.951 0.91013
Total 89 21.921 1.00000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Bray-Curtis is an abundance-weighted dissimilarity measure.
It is probably the most commonly used dissimilarity measure in microbiome research.
psx_braypsExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 178 taxa and 90 samples ]
sample_data() Sample Data: [ 90 samples by 20 sample variables ]
tax_table() Taxonomy Table: [ 178 taxa by 6 taxonomic ranks ]
psExtra info:
tax_agg = "Genus" tax_trans = "identity"
bray distance matrix of size 90
0.8294664 0.7156324 0.5111652 0.5492537 0.8991251 ...psx_bray %>%
ord_calc("PCoA") %>%
ord_plot(colour = "diagnosis") +
stat_ellipse(aes(colour = diagnosis)) +
coord_equal()
perm_bray <- psx_bray %>% dist_permanova(variables = "diagnosis")
perm_get(perm_bray)Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 2 1.5068 0.05441 2.5032 0.001 ***
Residual 87 26.1846 0.94559
Total 89 27.6914 1.00000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The phylogenetic distance family - has unweighted, weighted, and generalised versions.
You must use ASV-level data (i.e. no taxonomic aggregation) and have a phylogenetic tree available.
We will not practice with UniFrac distances today, because they can be quite slow to calculate.
The Aitchison distance is a CoDA distance method - named after John Aitchison, a pioneer in the field of Compositional Data analysis. related to CLR + PCA.
psx_aitchisonpsExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 178 taxa and 90 samples ]
sample_data() Sample Data: [ 90 samples by 20 sample variables ]
tax_table() Taxonomy Table: [ 178 taxa by 6 taxonomic ranks ]
psExtra info:
tax_agg = "Genus" tax_trans = "identity"
aitchison distance matrix of size 90
28.2123 18.57284 19.08465 21.43771 23.69247 ...psx_aitchison %>%
ord_calc("PCoA") %>%
ord_plot(colour = "diagnosis") +
stat_ellipse(aes(colour = diagnosis)) +
coord_equal()
perm_aitchison <- psx_aitchison %>% dist_permanova(variables = "diagnosis")
perm_get(perm_aitchison)Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 2 2552 0.10114 4.8946 0.001 ***
Residual 87 22681 0.89886
Total 89 25233 1.00000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1You can see from the PERMANOVA model outputs that the p value is below 0.05. So there is good statistical evidence that the bacterial gut microbiota composition of C-section delivered infants has a different composition than vaginally delivered infants at 4 days of age.
These terms are often used interchangeably.
Strictly, all distances are dissimilarities, but not all dissimilarities are distances.
A true “distance metric” \(d\), must satisfy 3 properties:
Identity of indiscernibles: For any samples \(a\) and \(b\), \(d(a, b) = 0\) if and only if \(a = b\)
Symmetry: For any samples \(a\) and \(b\), \(d(a, b) = d(b, a)\)
Triangle inequality: For any samples \(a\), \(b\), and \(c\), \(d(a, c) ≤ d(a, b) + d(b, c)\)
microViz often creates objects of class psExtra which store info about the aggregation and transformations you perform.
psExtra can also store a distance matrix (and an ordination or PERMANOVA results)dist_get()
099_AX 199_AX 062_BZ 194_AZ
099_AX 0.0000000 0.7173913 0.5588235 0.7241379
199_AX 0.7173913 0.0000000 0.7692308 0.8695652
062_BZ 0.5588235 0.7692308 0.0000000 0.6875000
194_AZ 0.7241379 0.8695652 0.6875000 0.0000000Notice how the Binary Jaccard dissimilarities range between 0 (identical) and 1 (no shared genera).
Principal Co-ordinates Analysis is one kind of ordination:
PCoA takes a sample-sample distance matrix and finds new dimensions (a coordinate system)
The new dimensions are created with the aim to preserve the original distances between samples
It also aims to capture the majority of this distance information in the first dimensions
This makes it easier to visualize the patterns in your data, in 2D scatterplots 👀
For more info, see “GUSTAME”
There is helpful info about ordination methods, including PCoA, on the GUide to STatistical Analysis in Microbial Ecology website (GUSTA ME). https://sites.google.com/site/mb3gustame/dissimilarity-based-methods/principal-coordinates-analysis
This website covers a lot of other topics too, which may be interesting for you to read at a later date if you’ll work on microbiome analysis.
“Permutational multivariate analysis of variance” - what does that mean?
You can adjust for covariates in PERMANOVA, and often should, depending on your study design.
Let’s fit a more complex model, adjusting for sex and age.
ps %>%
tax_agg(rank = "Genus") %>%
dist_calc(dist = "bray") %>%
dist_permanova(
variables = c("diagnosis", "gender", "age_years"),
n_perms = 999, seed = 111
) %>%
perm_get()2024-07-01 12:37:37.541204 - Starting PERMANOVA with 999 perms with 1 processes2024-07-01 12:37:37.906394 - Finished PERMANOVAPermutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 2 1.4591 0.05269 2.4103 0.001 ***
gender 1 0.1557 0.00562 0.5145 0.953
age_years 1 0.2899 0.01047 0.9577 0.472
Residual 85 25.7279 0.92909
Total 89 27.6914 1.00000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Use more permutations for a more precise and reliable p.value in your real work (it is slower).
Always set a seed number for reproducibility of this random permutation method!
We saw that diagnosis group is significantly associated with microbiota composition.
We probably also want to know if there are differences between each pair of diagnoses: CD, UC, Other.
From the previous ordination plot, we might hypothesise that UC shows the clearest difference.
psx_bray %>%
ord_calc("PCoA") %>%
ord_plot(colour = "diagnosis") +
stat_ellipse(aes(colour = diagnosis)) +
coord_equal()
There is no posthoc testing routine for PERMANOVA - so instead we will check each comparison individually.
We will use ps_filter() to exclude the samples from each diagnosis group each time.
ps %>%
ps_filter(diagnosis != "CD") %>%
tax_transform(trans = "identity", rank = "Genus") %>%
dist_calc("bray") %>%
dist_permanova(variables = "diagnosis", seed = 42)psExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 167 taxa and 67 samples ]
sample_data() Sample Data: [ 67 samples by 20 sample variables ]
tax_table() Taxonomy Table: [ 167 taxa by 6 taxonomic ranks ]
psExtra info:
tax_agg = "Genus" tax_trans = "identity"
bray distance matrix of size 67
0.8294664 0.5111652 0.5492537 0.8991251 0.9725358 ...
permanova:
Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 1 0.9927 0.04529 3.0832 0.005 **
Residual 65 20.9287 0.95471
Total 66 21.9214 1.00000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ps %>%
ps_filter(diagnosis != "UC") %>%
tax_transform(trans = "identity", rank = "Genus") %>%
dist_calc("bray") %>%
dist_permanova(variables = "diagnosis", seed = 42) psExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 145 taxa and 47 samples ]
sample_data() Sample Data: [ 47 samples by 20 sample variables ]
tax_table() Taxonomy Table: [ 145 taxa by 6 taxonomic ranks ]
psExtra info:
tax_agg = "Genus" tax_trans = "identity"
bray distance matrix of size 47
0.5969582 0.7538629 0.8122644 0.8410256 0.9814676 ...
permanova:
Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 1 0.2911 0.0248 1.1442 0.298
Residual 45 11.4500 0.9752
Total 46 11.7411 1.0000 ps %>%
ps_filter(diagnosis != "Other") %>%
tax_transform(trans = "identity", rank = "Genus") %>%
dist_calc("bray") %>%
dist_permanova(variables = "diagnosis", seed = 42) psExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 158 taxa and 66 samples ]
sample_data() Sample Data: [ 66 samples by 20 sample variables ]
tax_table() Taxonomy Table: [ 158 taxa by 6 taxonomic ranks ]
psExtra info:
tax_agg = "Genus" tax_trans = "identity"
bray distance matrix of size 66
0.7156324 0.5111652 0.5492537 0.8991251 0.8081828 ...
permanova:
Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 999
vegan::adonis2(formula = formula, data = metadata, permutations = n_perms, by = by, parallel = parall)
Df SumOfSqs R2 F Pr(>F)
diagnosis 1 0.8396 0.04031 2.6881 0.007 **
Residual 64 19.9905 0.95969
Total 65 20.8301 1.00000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Your methodological choices matter, so you should report what you did:
It’s a good idea to decide on one or two distance measures a priori, and report both (at least in supplementary material). The choice of distance measure can affect results and conclusions!
See this excellent online book chapter by Marti Anderson.
The GUide to STatistical Analysis in Microbial Ecology website
where PERMANOVA is called NP-MANOVA (non-parametric MANOVA).
microViz provides a Shiny app ord_explore() to interactively create and explore PCoA plots and other ordinations. Let’s give it a try!
To start the Shiny app, copy these lines to your Console (not the Quarto doc!)
# Note: we filter out OTUs that only appear in 1 sample, to speed up the app
ps %>%
tax_filter(min_prevalence = 2, verbose = FALSE) %>%
ord_explore()Colour the samples using the variables in the sample data
Select a few samples to view their composition on bar charts!
Change some ordination options:
Copy the automatically generated code
Launch the app again with a different subset of the data:
ps_filter()
ps %>%
tax_filter(min_prevalence = 2, verbose = FALSE) %>%
ps_filter(diagnosis == "UC") %>%
# calculate dominant Genus for each sample (optional)
ps_calc_dominant(rank = "Genus", none = "Mixed", other = "Other") %>%
ord_explore()To allow the interactive function to open a new tab in your browser, you may need to unblock pop-ups for posit.cloud
If you don’t see anything after running the ord_explore command, check for messages/notifications from your browser.
There are many distances available
Feel free to try out distances we haven’t talked about, BUT:
vegan and I haven’t tested them allThere are several other ordination methods available
Try out PCA, principal components analysis, which does NOT use distances
We will not discuss “constrained” or “conditioned” ordinations today, but if you are interested in e.g. RDA, check the Guide to Statistical Analysis in Microbial Ecology
“Principal Components Analysis”
For practical purposes, PCA is quite similar to Principal Co-ordinates Analysis.
In fact, PCA produces equivalent results to PCoA with Euclidean distances.
Euclidean distances are essentially a generalization of Pythagoras’ theorem to more dimensions.
In our data every taxon is a feature, a dimension, on which we calculate Euclidean distances.
Pythagoras’ theorem:
\[c = \sqrt{a^2 + b^2}\]
Euclidean distance:
\[d\left(p, q\right) = \sqrt{\sum _{i=1}^{n_{taxa}} \left( p_{i}-q_{i}\right)^2 }\]
Distance \(d\) between samples \(p\) and \(q\), with \(n\) taxa.
Principal components are built directly from a (linear) combination of the original features.
That means we know how much each taxon contributes to each PC dimension
We can plot this information (loadings) as arrows, alongside the sample points
pca <- ps %>%
tax_filter(min_prevalence = 2, verbose = FALSE) %>%
tax_transform(rank = "Genus", trans = "clr", zero_replace = "halfmin") %>%
ord_calc(method = "PCA") %>%
ord_plot(
alpha = 0.6, size = 2, color = "diagnosis",
plot_taxa = 1:6, tax_vec_length = 0.5,
tax_lab_style = tax_lab_style(
type = "text", max_angle = 90, aspect_ratio = 1,
size = 3, fontface = "bold"
),
) +
theme_classic(12) +
coord_fixed(ratio = 1, xlim = c(-3, 3), ylim = c(-3, 3), clip = "off")
pca
Interestingly, samples on the right of the plot (which tend to be UC patients) seem to have relatively more Escherichia/Shigella, and maybe less Blautia, Faecalibacterium and Roseburia.
When I run this code on my laptop, the UC patients are on the right of the PCA (and the Escherichia/Shigella loading arrow too)
But on your computer, the PCA plot might be mirrored, so they would be on the left side!
This is not a problem, as the sign (plus or minus) of a PC and its loadings is arbitrary, and the interpretation does not change.
This happens on different computers if they use slightly different software to solve linear algebra problems.
In general:
The relative length and direction of an arrow indicates how much that taxon contributes to the variation on each visible PC axis, e.g. Variation in Faecalibacterium abundance contributes quite a lot to variation along the PC1 axis.
The direction allows you to infer that samples positioned towards the left of the plot will tend to have higher relative abundance of Faecalibacterium than samples on the right of the plot.
Bacteroides variation contributes to both PC1 and PC2, as indicate by its high (negative) values on both axes.
But be cautious:
We can make another kind of bar plot, using the PCA information to order our samples in a circular layout.
This can help complement our interpretation of the PCA plot loadings.
iris <- ps %>%
tax_filter(min_prevalence = 2, verbose = FALSE) %>%
tax_transform(rank = "Genus", trans = "clr", zero_replace = "halfmin") %>%
ord_calc(method = "PCA") %>%
ord_plot_iris(
tax_level = "Genus", n_taxa = 12, other = "Other",
anno_colour = "diagnosis",
anno_colour_style = list(alpha = 0.6, size = 0.6, show.legend = FALSE)
)patchwork::wrap_plots(pca, iris, nrow = 1, guides = "collect")
These plots look weird! most samples bunch in the middle, with spindly projections..
Why doesn’t this work?
These ordinations are sensitive to sparsity (double-zero problem) -> aggregate taxa (and maybe filter rare taxa)
Excessive emphasis on high-abundance taxa -> log transform features first
Sequencing data are compositional -> try the centered log ratio (CLR) transformation
Remember, “Microbiome Datasets Are Compositional: And This Is Not Optional.” Gloor et al. 2017
The sequencing data gives us relative abundances, not absolute abundances.
The total number of reads sequenced per sample is an arbitrary total.
This leads to two main types of problem:
Statistical issues: taxon abundances are not independent, and may appear negatively correlated
Interpretation caveats: e.g. if one taxon blooms, the relative abundance of all other taxa will appear to decrease, even if they did not.
These issues are theoretically worse with simpler ecosystems (fewer taxa), e.g. vaginal microbiota.
The CLR transformation is useful for compositional microbiome data.
Problem: log(0) is undefined. So we need to do something about all the zeroes in our OTU table
Solution: add a small amount to every value (or just every zero), before applying the log transformation.
This small value is often called a pseudo-count.
What value should we use for the pseudo-count?
From the PCA loadings and the bar charts below, we have some suspicions about which Genera might differ in abundance in Case vs. Controls.
We can statistically test this for each taxon. This is often called “differential abundance” (DA) testing, in the style of “differential expression” (DE) testing from the transcriptomics field.
ps %>%
tax_transform("compositional") %>%
comp_barplot(
tax_level = "Genus", n_taxa = 12, facet_by = "diagnosis",
label = NULL, merge_other = FALSE
) +
coord_flip() +
theme(axis.ticks.y = element_blank())Registered S3 method overwritten by 'seriation':
method from
reorder.hclust vegan
More examples of visualizing microbiota compositions using stacked bar charts can be found here:
https://david-barnett.github.io/microViz/articles/web-only/compositions.html
We will start by creating a linear regression model for one genus-level category, Escherichia/Shigella.
We will fit a model with covariates, as we did for PERMANOVA
We will transform the count data by first making it proportions, and then taking a base 2 logarithm, log2, after adding a pseudocount.
escherReg <- ps %>%
tax_transform("compositional", rank = "Genus") %>%
tax_model(
type = "lm", rank = "Genus", taxa = "Escherichia/Shigella",
trans = "log2", trans_args = list(zero_replace = "halfmin"),
variables = c("IBD", "Female", "Age_Z"),
return_psx = FALSE
) %>%
pluck(1)Modelling: Escherichia/Shigellasummary(escherReg)
Call:
`Escherichia/Shigella` ~ IBD + Female + Age_Z
Residuals:
Min 1Q Median 3Q Max
-6.2823 -2.0197 -0.2065 2.9789 8.1094
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -12.3349 1.0546 -11.696 < 2e-16 ***
IBD 4.5143 1.0948 4.123 8.58e-05 ***
Female 0.4594 0.8614 0.533 0.595
Age_Z -0.2339 0.4859 -0.481 0.631
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.042 on 86 degrees of freedom
Multiple R-squared: 0.1864, Adjusted R-squared: 0.1581
F-statistic: 6.569 on 3 and 86 DF, p-value: 0.0004734The method we have used is borrowed from MaAsLin2 - developed by the Huttenhower lab at Harvard.
But, many other statistical methods have been developed for differential abundance analyses. Why?
Microbiota sequencing data are quite awkward, statistically, due to their sparseness and compositionality. Each successive method claims to handle some aspect of this awkwardness “better” than previous methods.
The aim is to have a method with adequate power to detect true associations, whilst controlling the type 1 error rate, the “false positive” reporting of associations that are not “truly” present.
Results are surprisingly inconsistent across different methods, as demonstrated recently in an analysis by Jacob Nearing et al.
We’re not normally interested in just one taxon
It’s also hard to decide which taxonomic rank we are most interested in modelling!
So now we will fit a similar model for almost every taxon* at every rank from phylum to genus
*We’ll filter out genera with a prevalence of less than 10%
We often want to filter out rare taxa before performing some kinds of analysis.
Rare taxa might sometimes be:
Overall, it’s less likely that we are interested in rare taxa, and models of rare taxon abundances are more likely to be unreliable.
Reducing the the number of taxa modelled also makes the process faster and makes visualizing the results easier!
What is rare?
How to pick a threshold, depends on what analysis method you are filtering for!
Let’s say we are not interested in Genera that occur in fewer than 10% of samples, and they have to have at least 100 reads in total across all samples.
Count genera before filtering
ntaxa(ps_genus) [1] 178Count genera after filtering
ps_genus %>%
tax_filter(min_prevalence = 0.1, min_total_abundance = 100) %>%
ntaxa() Proportional min_prevalence given: 0.1 --> min 9/90 samples.[1] 56Wow so that would remove most of our unique Genera!
What is going on? Let’s make some plots!
# first make a table of summary statistics for the unique genera
psGenusStats <- tibble(
taxon = taxa_names(ps_genus),
prevalence = microbiome::prevalence(ps_genus),
total_abundance = taxa_sums(ps_genus)
)
p <- psGenusStats %>%
ggplot(aes(total_abundance, prevalence)) +
geom_point(alpha = 0.5) +
geom_rug(alpha = 0.1) +
scale_x_log10(labels = scales::label_number(), name = "Total Abundance") +
scale_y_continuous(
labels = scales::label_percent(), breaks = scales::breaks_pretty(n = 9),
name = "Prevalence (%)",
sec.axis = sec_axis(
transform = ~ . * nsamples(ps),
breaks = scales::breaks_pretty(n = 9),
name = "Prevalence (N samples)"
)
) +
theme_bw()
p
So most Genera have a low prevalence, and handful have way more reads than most.
Let’s label those points to check which taxa are the big time players.
p + ggrepel::geom_text_repel(
data = function(df) filter(df, prevalence > 0.5 | total_abundance > 5000),
mapping = aes(label = taxon), size = 2, min.segment.length = 0
)
Those taxa make sense for this dataset of gut microbiota samples.
Now let’s zoom in on the less prevalent taxa by log-transforming the y axis.
We’ll also add lines indicating the thresholds of 10% prevalence and 1000 reads abundance.
psGenusStats %>%
ggplot(aes(x = total_abundance, y = prevalence)) +
geom_vline(xintercept = 100, color = "red", linetype = "dotted") +
geom_hline(yintercept = 10 / 100, color = "red", linetype = "dotted") +
geom_point(alpha = 0.5) +
geom_rug(alpha = 0.1) +
scale_x_log10(labels = scales::label_number(), name = "Total Abundance") +
scale_y_log10(
labels = scales::label_percent(),
breaks = scales::breaks_log(n = 9),
name = "Prevalence (%)",
sec.axis = sec_axis(
transform = ~ . * nsamples(ps),
breaks = scales::breaks_log(n = 9),
name = "Prevalence (N samples)"
)
) +
theme_bw()
We can break this down by phylum if we add the taxonomic table information.
# don't worry about this code, just focus on the plot output
ps_genus %>%
tax_table() %>%
as.data.frame() %>%
as_tibble(rownames = "taxon") %>%
left_join(psGenusStats, by = "taxon") %>%
add_count(Phylum, name = "phylum_count", sort = TRUE) %>%
mutate(Phylum = factor(Phylum, levels = unique(Phylum))) %>% # to fix facet order
mutate(Phylum = forcats::fct_lump_n(Phylum, n = 5)) %>%
mutate(Phylum = forcats::fct_na_value_to_level(Phylum, level = "Other")) %>%
ggplot(aes(total_abundance, prevalence)) +
geom_vline(xintercept = 100, color = "red", linetype = "dotted") +
geom_hline(yintercept = 10 / 100, color = "red", linetype = "dotted") +
geom_point(alpha = 0.5, size = 1) +
geom_rug(alpha = 0.2) +
scale_x_log10(
labels = scales::label_log(),
breaks = scales::breaks_log(n = 5),
name = "Total Abundance"
) +
scale_y_log10(
labels = scales::label_percent(),
breaks = scales::breaks_log(n = 9),
name = "Prevalence (%)",
sec.axis = sec_axis(
transform = ~ . * nsamples(shao19),
breaks = scales::breaks_log(n = 9),
name = "Prevalence (N samples)"
)
) +
facet_wrap("Phylum") +
theme_bw(10)
# The code for taxatree_models is quite similar to tax_model.
# tax_prepend_ranks ensures that each taxon at each rank is always unique.
psModels <- ps %>%
tax_prepend_ranks() %>%
tax_transform("compositional", rank = "Genus") %>%
tax_filter(min_prevalence = 0.1, undetected = 0) %>%
taxatree_models(
type = lm,
trans = "log2", trans_args = list(zero_replace = "halfmin"),
ranks = c("Phylum", "Class", "Order", "Family", "Genus"),
variables = c("IBD", "Female", "Age_Z")
)psModelspsExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 65 taxa and 90 samples ]
sample_data() Sample Data: [ 90 samples by 23 sample variables ]
tax_table() Taxonomy Table: [ 65 taxa by 6 taxonomic ranks ]
otu_get(counts = TRUE) [ 65 taxa and 90 samples ]
psExtra info:
tax_agg = "Genus" tax_trans = "compositional"
taxatree_models list:
Ranks: Phylum/Class/Order/Family/GenusNext we will get a data.frame containing the regression coefficient estimates, test statistics and corresponding p values from all these regression models.
psStats <- taxatree_models2stats(psModels)
psStatspsExtra object - a phyloseq object with extra slots:
phyloseq-class experiment-level object
otu_table() OTU Table: [ 65 taxa and 90 samples ]
sample_data() Sample Data: [ 90 samples by 23 sample variables ]
tax_table() Taxonomy Table: [ 65 taxa by 6 taxonomic ranks ]
otu_get(counts = TRUE) [ 65 taxa and 90 samples ]
psExtra info:
tax_agg = "Genus" tax_trans = "compositional"
taxatree_stats dataframe:
126 taxa at 5 ranks: Phylum, Class, Order, Family, Genus
3 terms: IBD, Female, Age_ZpsStats %>% taxatree_stats_get()# A tibble: 378 × 8
term taxon rank formula estimate std.error statistic p.value
<fct> <chr> <fct> <chr> <dbl> <dbl> <dbl> <dbl>
1 IBD P: Firmicutes Phylum `P: Fir… -0.626 0.332 -1.89 6.25e-2
2 Female P: Firmicutes Phylum `P: Fir… -0.391 0.261 -1.50 1.37e-1
3 Age_Z P: Firmicutes Phylum `P: Fir… 0.151 0.147 1.02 3.09e-1
4 IBD P: Proteobacteria Phylum `P: Pro… 4.20 0.950 4.42 2.89e-5
5 Female P: Proteobacteria Phylum `P: Pro… 0.778 0.747 1.04 3.01e-1
6 Age_Z P: Proteobacteria Phylum `P: Pro… -0.568 0.422 -1.35 1.81e-1
7 IBD P: Bacteroidetes Phylum `P: Bac… -1.75 1.17 -1.49 1.39e-1
8 Female P: Bacteroidetes Phylum `P: Bac… -0.802 0.922 -0.870 3.87e-1
9 Age_Z P: Bacteroidetes Phylum `P: Bac… -0.181 0.520 -0.348 7.29e-1
10 IBD P: Actinobacteria Phylum `P: Act… -1.67 0.916 -1.82 7.18e-2
# ℹ 368 more rowsWe have performed a lot of statistical tests here, so it is likely that we could find some significant p-values by chance alone.
We should correct for multiple testing / control the false discovery rate or family-wise error rate.
Instead of applying these adjustment methods across all taxa models at all ranks, the default behaviour is to control the family-wise error rate per taxonomic rank.
psStats <- psStats %>% taxatree_stats_p_adjust(method = "BH", grouping = "rank")
# notice the new variable
psStats %>% taxatree_stats_get()# A tibble: 378 × 9
# Groups: rank [5]
term taxon rank formula estimate std.error statistic p.value p.adj.BH.rank
<fct> <chr> <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 IBD P: F… Phyl… `P: Fi… -0.626 0.332 -1.89 6.25e-2 0.188
2 Female P: F… Phyl… `P: Fi… -0.391 0.261 -1.50 1.37e-1 0.291
3 Age_Z P: F… Phyl… `P: Fi… 0.151 0.147 1.02 3.09e-1 0.496
4 IBD P: P… Phyl… `P: Pr… 4.20 0.950 4.42 2.89e-5 0.000607
5 Female P: P… Phyl… `P: Pr… 0.778 0.747 1.04 3.01e-1 0.496
6 Age_Z P: P… Phyl… `P: Pr… -0.568 0.422 -1.35 1.81e-1 0.346
7 IBD P: B… Phyl… `P: Ba… -1.75 1.17 -1.49 1.39e-1 0.291
8 Female P: B… Phyl… `P: Ba… -0.802 0.922 -0.870 3.87e-1 0.496
9 Age_Z P: B… Phyl… `P: Ba… -0.181 0.520 -0.348 7.29e-1 0.729
10 IBD P: A… Phyl… `P: Ac… -1.67 0.916 -1.82 7.18e-2 0.188
# ℹ 368 more rowstaxatree_plots allows you to plot statistics from all of the taxa models onto a tree layout (e.g. point estimates and significance).
The taxon model results are organised by rank, radiating out from the central root node e.g. from Phyla around the center to Genus in the outermost ring.
taxatree_plots itself returns a list of plots, which you can arrange into one figure with the patchwork package and/or cowplot.
psStats %>%
taxatree_plots(node_size_range = c(1, 3), sig_stat = "p.adj.BH.rank") %>%
patchwork::wrap_plots(ncol = 2, guides = "collect")
But how do we know which taxa are which nodes? We can create a labelled grey tree with taxatree_plotkey. This labels only some of the taxa based on certain conditions that we specify.
set.seed(123) # label position
key <- psStats %>%
taxatree_plotkey(
taxon_renamer = function(x) stringr::str_remove(x, "[PFG]: "),
# conditions below, for filtering taxa to be labelled
rank == "Phylum" | rank == "Genus" & prevalence > 0.2
# all phyla are labelled, and all genera with a prevalence of over 0.2
)
key
You can learn how to customise these tree plots to your needs, with this extended tutorial on the microViz website
If you have already carefully gone through everything above, you may be ready for a real challenge.
Is current disease activity level associated with microbiota diversity, composition, or the relative abundance of specific taxa?
Are IBD-related medications associated with microbiota diversity, composition, or the relative abundance of specific taxa?
No code is provided for this challenge - just suggestions.
IBD is characterised by periods of active symptomatic disease interspersed with inactive or less symptomatic periods.
It is reasonable to hypothesise that microbiota dysbiosis might be more pronounced during periods of high activity.
Try looking at only the IBD patients (i.e. filter out the controls) to assess if disease activity is associated with microbiota diversity or composition.
Tip: A good place to start is with ps_filter and ord_explore
Several patients recently took antibiotics, or corticosteroids or other immunosuppressive medications.
These medications are often used to manage symptoms or slow disease progression in IBD.
It is also reasonable to hypothesise that they might affect the gut microbiota composition.
Try creating a correlation heatmap to assess associations between the abundance of top genera and each medication.
Look at this tutorial article for ideas:
https://david-barnett.github.io/microViz/articles/web-only/heatmaps.html#correlation-heatmaps
Tip 1: Convert each variable to binary integers: 0 for medication not used, 1 for medication used.
Tip 2: Use a non-parametric correlation measure, and don’t include too many taxa.
The final challenge awaits in Practical 3, which you can start after the metagenomics lecture.
david-barnett.github.io/2024-NUTRIM-microbiome/practical-3/web/practical3-instructions.html
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